Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-x64cq Total loading time: 0.414 Render date: 2022-05-25T16:58:43.624Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

Toward a generalized notion of discrete time for modeling temporal networks

Published online by Cambridge University Press:  25 January 2022

Konstantin Kueffner
Affiliation:
Vienna University of Economics and Business, WU, Vienna, Austria Secure Business Austria Research Center (SBA), Vienna, Austria
Mark Strembeck*
Affiliation:
Vienna University of Economics and Business, WU, Vienna, Austria Secure Business Austria Research Center (SBA), Vienna, Austria Complexity Science Hub Vienna (CSH), Vienna, Austria
*
*Corresponding author. Email: mark.strembeck@wu.ac.at
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many real-world networks, including social networks and computer networks for example, are temporal networks. This means that the vertices and edges change over time. However, most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of discrete time for modeling temporal networks. Our approach also allows for considering nondeterministic time and incomplete data, two issues that are often found when analyzing datasets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks. In addition, we implemented an R-package that provides programming support for all concepts discussed in this paper. The R-package is publicly available for download.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

Action Editor: Ulrik Brandes

References

Ahuja, M., & Malhi, H. (2016). Predicting links in complex network using fuzzy logic. International Journal of Computer Trends and Technology, 36, 158162.CrossRefGoogle Scholar
Aleta, A., & Moreno, Y. (2018). Multilayer networks in a nutshell. Annual Review of Condensed Matter Physics, 10, 4562.CrossRefGoogle Scholar
Badie-Modiri, A., Karsai, M., & KivelÄ, M. (2020). Efficient limited-time reachability estimation in temporal networks. Physical Review E, 101(5), 052303.CrossRefGoogle ScholarPubMed
Barbehenn, M. (1998). A note on the complexity of dijkstra’s algorithm for graphs with weighted vertices. IEEE Transactions on Computers, 47(2), 263.CrossRefGoogle Scholar
Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C. I., GÓmez-Gardenes, J., Romance, M., Sendina-Nadal, I., Wang, Z., & Zanin, M. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1), 1122.CrossRefGoogle ScholarPubMed
Bochman, A. (2011). Logic in nonmonotonic reasoning. In Nonmonotonic reasoning. Essays celebrating its 30th anniversary (pp. 25–61). Rickmansworth, England: College Publications.Google Scholar
Buccafurri, F., & Caminiti, G. (2005). A social semantics for multi-agent systems. In International conference on logic programming and nonmonotonic reasoning (pp. 317–329). Berlin, Heidelberg: Springer.Google Scholar
Burgess, J. P. (1979). Logic and time 1. The Journal of Symbolic Logic, 44(4), 566582.CrossRefGoogle Scholar
Casteigts, A., Flocchini, P., Quattrociocchi, W., & Santoro, N. (2012). Time-varying graphs and dynamic networks. International Journal of Parallel, Emergent and Distributed Systems, 27(5), 387408.CrossRefGoogle Scholar
Cau, A., Moszkowski, B., & Zedan, H. (2006). Interval temporal logic. Retrieved from http://www. cms. dmu. ac. uk/cau/itlhomepage/itlhomepage.html.Google Scholar
Cliffe, O., De Vos, M., & Padget, J. (2005). Specifying and analysing agent-based social institutions using answer set programming. In International conference on autonomous agents and multiagent systems (pp. 99–113). Berlin, Heidelberg: Springer.Google Scholar
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms . Cambridge, MA and London, England: MIT Press.Google Scholar
Costantini, S., & Tocchio, A. (2004). The dali logic programming agent-oriented language. In European workshop on logics in artificial intelligence (pp. 685–688). Berlin, Heidelberg: Springer.Google Scholar
Cozzo, E., de Arruda, G. F., Rodrigues, F. A., & Moreno, Y. (2016). Multilayer networks: Metrics and spectral properties. In Interconnected networks (pp. 17–35). Berlin, Heidelberg: Springer.Google Scholar
Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems, 1695(5), 19.Google Scholar
De Domenico, M., SolÉ-Ribalta, A., Cozzo, E., KivelÄ, M., Moreno, Y., Porter, M. A., GÓmez, S., & Arenas, A. (2013). Mathematical formulation of multilayer networks. Physical Review X, 3(4), 041022.CrossRefGoogle Scholar
De Vos, M., & Vermeir, D. (2003). Logic programming agents playing games. In Research and development in intelligent systems XIX (pp. 323–336). Berlin, Heidelberg: Springer.Google Scholar
Dickson, L. E. (1913). Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American Journal of Mathematics, 35(4), 413422.CrossRefGoogle Scholar
Fenu, C., & Higham, D. J. (2017). Block matrix formulations for evolving networks. SIAM Journal on Matrix Analysis and Applications, 38(2), 343360.CrossRefGoogle Scholar
GÖdel, K. (1949). An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Reviews of Modern Physics, 21(3), 447.CrossRefGoogle Scholar
Goranko, V., & Galton, A. (2015). Temporal logic. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (winter 2015 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Goshtasby, A. A. (2012). Similarity and dissimilarity measures. In Image registration (pp. 7–66). Berlin, Heidelberg: Springer.Google Scholar
Gottlob, G. (1992). Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3), 397425.CrossRefGoogle Scholar
Holme, P., & SaramÄki, J. (2012). Temporal networks. Physics Reports, 519(3), 97125.CrossRefGoogle Scholar
Kempe, D., Kleinberg, J., & Kumar, A. (2002). Connectivity and inference problems for temporal networks. Journal of Computer and System Sciences, 64(4), 820842.CrossRefGoogle Scholar
KivelÄ, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203271.CrossRefGoogle Scholar
KivelÄ, M., Cambe, J., SaramÄki, J., & Karsai, M. (2018). Mapping temporal-network percolation to weighted, static event graphs. Scientific Reports, 8(1), 19.CrossRefGoogle ScholarPubMed
KivelÄ, M. & Porter, M. A. (2018). Isomorphisms in multilayer networks. IEEE Transactions on Network Science and Engineering, 5(3), 198211.CrossRefGoogle Scholar
Kostakos, V. (2009). Temporal graphs. Physica A: Statistical Mechanics and its Applications, 388(6), 10071023.CrossRefGoogle Scholar
KrÖger, F. (2012). Temporal logic of programs, vol. 8. Berlin, Heidelberg: Springer Science & Business Media.Google Scholar
Kueffner, K. & Strembeck, M. (2019). A generalized notion of time for modeling temporal networks. In Proceedings of the 4th international conference on complexity, future information systems and risk (COMPLEXIS). SetÚbal, Portugal.CrossRefGoogle Scholar
Latapy, M., Viard, T., & Magnien, C. (2018). Stream graphs and link streams for the modeling of interactions over time. Social Network Analysis and Mining, 8(1), 129.CrossRefGoogle Scholar
Lopes, N. P., BjØrner, N., Godefroid, P., Jayaraman, K., & Varghese, G. (2015). Checking beliefs in dynamic networks. In 12th {USENIX} symposium on networked systems design and implementation ({NSDI} 15) (pp. 499–512). Berkeley, CA.Google Scholar
Markosian, N., Sullivan, M., & Emery, N. (2016). Time. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (fall 2016 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Matthews, S. G. (1994). Partial metric topology. Annals of the New York Academy of Sciences, 728(1), 183197.CrossRefGoogle Scholar
Mellor, A. (2018). The temporal event graph. Journal of Complex Networks, 6(4), 639659.CrossRefGoogle Scholar
Michail, O. (2016). An introduction to temporal graphs: An algorithmic perspective. Internet Mathematics, 12(4), 239280.CrossRefGoogle Scholar
Monteiro, P. T., Ropers, D., Mateescu, R., Freitas, A. T., & De Jong, H. (2008). Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics, 24(16), i227i233.CrossRefGoogle ScholarPubMed
Panda, A., Argyraki, K., Sagiv, M., Schapira, M., & Shenker, S. (2015). New directions for network verification. In 1st summit on advances in programming languages (SNAPL 2015). Dagstuhl, Germany: Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.Google Scholar
Pardo, R., SÁnchez, C., & Schneider, G. (2018). Timed epistemic knowledge bases for social networks. In International symposium on formal methods (pp. 185–202). Berlin, Heidelberg: Springer.Google Scholar
Plotkin, G. D., BjØrner, N., Lopes, N. P., Rybalchenko, A., & Varghese, G. (2016). Scaling network verification using symmetry and surgery. ACM SIGPLAN Notices, 51(1), 6983.CrossRefGoogle Scholar
Runkler, T. A. (2012). Data analytics. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
Schroeder, V. (2006). Quasi-metric and metric spaces. Conformal Geometry and Dynamics of the American Mathematical Society, 10(18), 355360.CrossRefGoogle Scholar
Segarra, S., & Ribeiro, A. (2016). Stability and continuity of centrality measures in weighted graphs. IEEE Transactions on Signal Processing, 64(3), 543555.CrossRefGoogle Scholar
Seligman, J., Liu, F., & Girard, P. (2011). Logic in the community. In Indian conference on logic and its applications (pp. 178–188). Berlin, Heidelberg: Springer.Google Scholar
SolÁ, L., Romance, M., Criado, R., Flores, J., Garca del Amo, A., & Boccaletti, S. (2013). Eigenvector centrality of nodes in multiplex networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(3), 033131.CrossRefGoogle ScholarPubMed
SolÉ-Ribalta, A., De Domenico, M., GÓmez, S., & Arenas, A. (2016). Random walk centrality in interconnected multilayer networks. Physica D: Nonlinear Phenomena, 323, 7379.CrossRefGoogle Scholar
Spatocco, C., Stilo, G., & Domeniconi, C. (2018). A new framework for centrality measures in multiplex networks. arXiv preprint arXiv:1801.08026.Google Scholar
Sunitha, M., & Mathew, S. (2013). Fuzzy graph theory: A survey. Annals of Pure and Applied mathematics, 4(1), 92110.Google Scholar
Tang, J., Musolesi, M., Mascolo, C., & Latora, V. (2009). Temporal distance metrics for social network analysis. In Proceedings of the 2nd ACM workshop on Online social networks (pp. 31–36). New York City, NY: ACM.Google Scholar
Tarapata, Z. (2007). Selected multicriteria shortest path problems: An analysis of complexity, models and adaptation of standard algorithms. International Journal of Applied Mathematics and Computer Science, 17(2), 269287.CrossRefGoogle Scholar
Taylor, D., Myers, S. A., Clauset, A., Porter, M. A., & Mucha, P. J. (2017). Eigenvector-based centrality measures for temporal networks. Multiscale Modeling & Simulation, 15(1), 537574.CrossRefGoogle ScholarPubMed
Tomasini, M. (2015). An introduction to multilayer networks. BioComplex Laboratory, Florida Institute of Technology, Melbourne, USA (pp. 114).Google Scholar
Van Benthem, J. (2014). Logic in games. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Van Benthem, J., van Benthem, J. F., van Benthem, J. F., MathÉmaticien, I., & van Benthem, J. F. (2010). Modal logic for open minds. Stanford, CA: Center for the Study of Language and Information Stanford.Google Scholar
Van Ditmarsch, H., van Der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic, vol. 337. Berlin, Heidelberg: Springer Science & Business Media.Google Scholar
Venema, Y. (2017). Temporal logic (pp. 203223), chapter 10. Hoboken, NJ: John Wiley & Sons, Ltd.Google Scholar
Wang, D., Wang, H., & Zou, X. (2017). Identifying key nodes in multilayer networks based on tensor decomposition. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(6), 063108.CrossRefGoogle ScholarPubMed
Wickham, H. (2014). Advanced R . Chapman & Hall/CRC The R Series. Boca Raton, FL: CRC Press.Google Scholar
Wickham, H. (2015). R packages: organize, test, document, and share your code. London, UK: O’Reilly Media, Inc.Google Scholar
Wu, H., Cheng, J., Huang, S., Ke, Y., Lu, Y., & Xu, Y. (2014). Path problems in temporal graphs. Proceedings of the VLDB Endowment, 7(9), 721732.CrossRefGoogle Scholar
You have Access
Open access

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Toward a generalized notion of discrete time for modeling temporal networks
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Toward a generalized notion of discrete time for modeling temporal networks
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Toward a generalized notion of discrete time for modeling temporal networks
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *